Internal problem ID [10210]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IV, differential equations of the first order and higher degree than the first. Article
27. Clairaut equation. Page 56
Problem number: Ex 9.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {\left (x -y^{\prime }-y\right )^{2}-x^{2} \left (-x^{2} y^{\prime }+2 y x \right )=0} \end {gather*}
✗ Solution by Maple
dsolve((x-diff(y(x),x)-y(x))^2=x^2*(2*x*y(x)-x^2*diff(y(x),x)),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(x-y'[x]-y[x])^2==x^2*(2*x*y[x]-x^2*y'[x]),y[x],x,IncludeSingularSolutions -> True]
Not solved